public void zero_inliers_test()
{
// Fix the random number generator
Accord.Math.Random.Generator.Seed = 0;
double[,] data = // This is the same data used in the RANSAC sample app
{
{ 1.0, 0.79 }, { 3, 2.18 }, { 5, 5.99 }, { 7.0, 7.65 },
{ 9.0, 9.55 }, { 11, 11.89 }, { 13, 13.73 }, { 15.0, 14.77 },
{ 17.0, 18.00 }, { 1.2, 1.45 }, { 1.5, 1.18 }, { 1.8, 1.92 },
{ 2.1, 1.47 }, { 2.4, 2.41 }, { 2.7, 2.35 }, { 3.0, 3.41 },
{ 3.3, 3.78 }, { 3.6, 3.21 }, { 3.9, 4.76 }, { 4.2, 5.03 },
{ 4.5, 4.19 }, { 4.8, 3.81 }, { 5.1, 6.07 }, { 5.4, 5.74 },
{ 5.7, 6.39 }, { 6, 6.11 }, { 6.3, 6.86 }, { 6.6, 6.35 },
{ 6.9, 7.9 }, { 7.2, 8.04 }, { 7.5, 8.48 }, { 7.8, 8.07 },
{ 8.1, 8.22 }, { 8.4, 8.41 }, { 8.7, 9.4 }, { 9, 8.8 },
{ 9.3, 8.44 }, { 9.6, 9.32 }, { 9.9, 9.18 }, { 10.2, 9.86 },
{ 10.5, 10.16 }, { 10.8, 10.28 }, { 11.1, 11.07 }, { 11.4, 11.66 },
{ 11.7, 11.13 }, { 12, 11.55 }, { 12.3, 12.62 }, { 12.6, 12.27 },
{ 12.9, 12.33 }, { 13.2, 12.37 }, { 13.5, 12.75 }, { 13.8, 14.44 },
{ 14.1, 14.71 }, { 14.4, 13.72 }, { 14.7, 14.54 }, { 15, 14.67 },
{ 15.3, 16.04 }, { 15.6, 15.21 }, { 1, 3.9 }, { 2, 11.5 },
{ 3.0, 13.0 }, { 4, 0.9 }, { 5, 5.5 }, { 6, 16.2 },
{ 7.0, 0.8 }, { 8, 9.4 }, { 9, 9.5 }, { 10, 17.5 },
{ 11.0, 6.3 }, { 12, 12.6 }, { 13, 1.5 }, { 14, 1.5 },
{ 2.0, 10 }, { 3, 9 }, { 15, 2 }, { 15.5, 1.2 },
};
// First, fit simple linear regression directly for comparison reasons.
double[] x = data.GetColumn(0); // Extract the independent variable
double[] y = data.GetColumn(1); // Extract the dependent variable
// Create a simple linear regression
var regression = new SimpleLinearRegression();
// Estimate a line passing through the (x, y) points
double sumOfSquaredErrors = regression.Regress(x, y);
// Now, compute the values predicted by the
// regression for the original input points
double[] commonOutput = regression.Compute(x);
// Now, fit simple linear regression using RANSAC
int maxTrials = 1000;
int minSamples = 20;
double probability = 0.950;
double errorThreshold = 1000;
int count = 0;
// Create a RANSAC algorithm to fit a simple linear regression
var ransac = new RANSAC<SimpleLinearRegression>(minSamples)
{
Probability = probability,
Threshold = errorThreshold,
MaxEvaluations = maxTrials,
// Define a fitting function
Fitting = delegate(int[] sample)
{
// Retrieve the training data
double[] inputs = x.Submatrix(sample);
double[] outputs = y.Submatrix(sample);
// Build a Simple Linear Regression model
var r = new SimpleLinearRegression();
r.Regress(inputs, outputs);
return r;
},
// Define a check for degenerate samples
Degenerate = delegate(int[] sample)
{
// In this case, we will not be performing such checks.
return false;
},
// Define a inlier detector function
Distances = delegate(SimpleLinearRegression r, double threshold)
{
count++;
List<int> inliers = new List<int>();
// Generate 0 inliers twice, then proceed as normal
if (count > 2)
{
for (int i = 0; i < x.Length; i++)
{
// Compute error for each point
double error = r.Compute(x[i]) - y[i];
// If the squared error is below the given threshold,
// the point is considered to be an inlier.
if (error * error < threshold)
inliers.Add(i);
}
}
return inliers.ToArray();
}
};
// Now that the RANSAC hyperparameters have been specified, we can
// compute another regression model using the RANSAC algorithm:
int[] inlierIndices;
SimpleLinearRegression robustRegression = ransac.Compute(data.Rows(), out inlierIndices);
// Compute the output of the model fitted by RANSAC
double[] ransacOutput = robustRegression.Compute(x);
Assert.AreEqual(ransac.TrialsNeeded, 0);
Assert.AreEqual(ransac.TrialsPerformed, 3);
string a = inlierIndices.ToCSharp();
string b = ransacOutput.ToCSharp();
int[] expectedInliers = new int[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75 };
double[] expectedOutput = new double[] { 4.62124895918799, 5.37525473445784, 6.12926050972769, 6.88326628499754, 7.63727206026739, 8.39127783553724, 9.14528361080709, 9.89928938607694, 10.6532951613468, 4.69664953671498, 4.80975040300545, 4.92285126929593, 5.03595213558641, 5.14905300187689, 5.26215386816736, 5.37525473445784, 5.48835560074832, 5.6014564670388, 5.71455733332927, 5.82765819961975, 5.94075906591023, 6.05385993220071, 6.16696079849118, 6.28006166478166, 6.39316253107214, 6.50626339736262, 6.61936426365309, 6.73246512994357, 6.84556599623405, 6.95866686252453, 7.071767728815, 7.18486859510548, 7.29796946139596, 7.41107032768644, 7.52417119397691, 7.63727206026739, 7.75037292655787, 7.86347379284835, 7.97657465913882, 8.0896755254293, 8.20277639171978, 8.31587725801026, 8.42897812430073, 8.54207899059121, 8.65517985688169, 8.76828072317216, 8.88138158946264, 8.99448245575312, 9.1075833220436, 9.22068418833408, 9.33378505462455, 9.44688592091503, 9.55998678720551, 9.67308765349599, 9.78618851978646, 9.89928938607694, 10.0123902523674, 10.1254911186579, 4.62124895918799, 4.99825184682292, 5.37525473445784, 5.75225762209277, 6.12926050972769, 6.50626339736262, 6.88326628499754, 7.26026917263247, 7.63727206026739, 8.01427494790232, 8.39127783553724, 8.76828072317216, 9.14528361080709, 9.52228649844202, 4.99825184682292, 5.37525473445784, 9.89928938607694, 10.0877908298944 };
Assert.IsTrue(inlierIndices.IsEqual(expectedInliers));
Assert.IsTrue(ransacOutput.IsEqual(expectedOutput, 1e-10));
}
